Package edu.jas.gbufd

Interface Syzygy<C extends RingElem<C>>

Type Parameters:
C - coefficient type
All Superinterfaces:
Serializable
All Known Implementing Classes:
SyzygyAbstract, SyzygySeq

public interface Syzygy<C extends RingElem<C>> extends Serializable
Syzygy interface. Defines Syzygy computations and tests.
  • Method Details

    • zeroRelations

      List<List<GenPolynomial<C>>> zeroRelations(List<GenPolynomial<C>> F)
      Syzygy module from Groebner base. F must be a Groebner base.
      Parameters:
      F - a Groebner base.
      Returns:
      syz(F), a basis for the module of syzygies for F.
    • zeroRelations

      List<List<GenPolynomial<C>>> zeroRelations(int modv, List<GenPolynomial<C>> F)
      Syzygy module from Groebner base. F must be a Groebner base.
      Parameters:
      modv - number of module variables.
      F - a Groebner base.
      Returns:
      syz(F), a basis for the module of syzygies for F.
    • zeroRelations

      List<List<GenPolynomial<C>>> zeroRelations(int modv, GenVector<GenPolynomial<C>> v)
      Syzygy module from Groebner base. v must be a Groebner base.
      Parameters:
      modv - number of module variables.
      v - a Groebner base.
      Returns:
      syz(v), a basis for the module of syzygies for v.
    • zeroRelations

      ModuleList<C> zeroRelations(ModuleList<C> M)
      Syzygy module from module Groebner base. M must be a module Groebner base.
      Parameters:
      M - a module Groebner base.
      Returns:
      syz(M), a basis for the module of syzygies for M.
    • isZeroRelation

      boolean isZeroRelation(List<List<GenPolynomial<C>>> Z, List<GenPolynomial<C>> F)
      Test if sysygy.
      Parameters:
      Z - list of sysygies.
      F - a polynomial list.
      Returns:
      true, if Z is a list of syzygies for F, else false.
    • isZeroRelation

      boolean isZeroRelation(ModuleList<C> Z, ModuleList<C> F)
      Test if sysygy of modules.
      Parameters:
      Z - list of sysygies.
      F - a module list.
      Returns:
      true, if Z is a list of syzygies for F, else false.
    • resolution

      List<ResPart<C>> resolution(ModuleList<C> M)
      Resolution of a module. Only with direct GBs.
      Parameters:
      M - a module list of a Groebner basis.
      Returns:
      a resolution of M.
    • resolution

      List resolution(PolynomialList<C> F)
      Resolution of a polynomial list. Only with direct GBs.
      Parameters:
      F - a polynomial list of a Groebner basis.
      Returns:
      a resolution of F.
    • resolutionArbitrary

      List resolutionArbitrary(PolynomialList<C> F)
      Resolution of a polynomial list.
      Parameters:
      F - a polynomial list of an arbitrary basis.
      Returns:
      a resolution of F.
    • resolutionArbitrary

      List<ResPart<C>> resolutionArbitrary(ModuleList<C> M)
      Resolution of a module.
      Parameters:
      M - a module list of an arbitrary basis.
      Returns:
      a resolution of M.
    • zeroRelationsArbitrary

      List<List<GenPolynomial<C>>> zeroRelationsArbitrary(List<GenPolynomial<C>> F)
      Syzygy module from arbitrary base.
      Parameters:
      F - a polynomial list.
      Returns:
      syz(F), a basis for the module of syzygies for F.
    • zeroRelationsArbitrary

      List<List<GenPolynomial<C>>> zeroRelationsArbitrary(int modv, List<GenPolynomial<C>> F)
      Syzygy module from arbitrary base.
      Parameters:
      modv - number of module variables.
      F - a polynomial list.
      Returns:
      syz(F), a basis for the module of syzygies for F.
    • zeroRelationsArbitrary

      ModuleList<C> zeroRelationsArbitrary(ModuleList<C> M)
      Syzygy module from arbitrary module base.
      Parameters:
      M - an arbitrary module base.
      Returns:
      syz(M), a basis for the module of syzygies for M.